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About: Pseudo-abelian category     Goto   Sponge   NotDistinct   Permalink

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In mathematics, specifically in category theory, a pseudo-abelian category is a category that is preadditive and is such that every idempotent has a kernel. Recall that an idempotent morphism is an endomorphism of an object with the property that . Elementary considerations show that every idempotent then has a cokernel. The pseudo-abelian condition is stronger than preadditivity, but it is weaker than the requirement that every morphism have a kernel and cokernel, as is true for abelian categories. Synonyms in the literature for pseudo-abelian include pseudoabelian and Karoubian.